Dividing a Decimal Number into a Decimal Fraction

To divide a decimal number by another decimal number, we can follow the steps below:

Step 1: Convert the Decimal Number into a Decimal Fraction

To convert a decimal number into a decimal fraction, we need to identify the place value of the decimal digits. The place value of the digits to the right of the decimal point decreases from left to right, with the first digit to the right of the decimal point being in the tenths place, the second digit in the hundredths place, the third digit in the thousandths place, and so on.

For example, if we have the decimal number 3.25, we can convert it into a decimal fraction as follows:

3.25 = 3 + 0.2 + 0.05

The whole number part, which is 3, remains the same. The decimal part, 0.2, can be written as 2/10 or 1/5, and the decimal part 0.05 can be written as 5/100 or 1/20.

Therefore, 3.25 can be written as the decimal fraction 3 + 1/5 + 1/20.

Step 2: Dividing the Decimal Fraction

Once we have converted the decimal number into a decimal fraction, we can divide it by another decimal number. To do this, we can follow the normal division process, using long division or any other method.

For example, let's say we want to divide 3.25 by 1.5. We can write it as:

3 + 1/5 + 1/20 ÷ 1.5

Using long division, we divide the whole number part first:

2 divided by 1 equals 2

Next, we bring down the next digit, which is 5:

5 divided by 1 equals 5

Now, we have a remainder of 5. To continue dividing, we can add a zero after the decimal point and bring it down:

50 divided by 15 equals 3 remainder 5

We continue this process until we reach the desired level of precision or until the remainder becomes zero.

Step 3: Expressing the Quotient as a Decimal Number

After dividing the decimal fraction, we obtain a quotient. To express this quotient as a decimal number, we need to convert the fraction part back into decimal form.

In the example above, the quotient is 2.35. We can convert the fraction 1/20 into decimal form by dividing 1 by 20:

1 divided by 20 equals 0.05

Therefore, the final quotient is 2.35.

Summary:

To divide a decimal number by another decimal number, we can first convert the decimal number into a decimal fraction. Then, we divide the decimal fraction using the standard division process. Finally, we express the quotient as a decimal number by converting any remaining fractions into decimal form.

By following these steps, we can divide decimal numbers and express the quotient as a decimal number.